Efficiency and the Redistribution of Welfare
Vasilis Syrgkanis2011
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Abstract
We examine how the relation between individual and social utility affect the efficiency of game-theoretic solution concepts. We first provide general results for monotone utility-maximization games, showing that if each player's utility is at least his marginal contribution to the welfare, then the social welfare in any Strong Nash Equilibrium is at least half of the optimal. The efficiency degrades smoothly as the marginal contribution assumption is relaxed. For non-monotone utility maximization games, we manage to give efficiency results if the game is also a potential game. We also extend previous results on efficiency of Nash Equilibria for the case when social welfare is submodular.
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